Von Miller, of the Denver Broncos, has been suspended for six games of the NFL season. Photograph: Jack Dempsey/AP

On the eve of the NFL's latest showpiece game at Wembley the World Anti-Doping Agency has warned American football that its drugs policy needs to be more transparent otherwise people will believe the sport has "something to hide".

David Howman, the director-general of Wada, also voiced his frustration that blood-testing for human growth hormone in the NFL had been delayed by the players' union, who had tried "every possible way to avoid testing".

Twenty-six players were suspended in 2012 for violating the NFL's substance abuse policy, a figure some commentators have suggested would be far higher if blood tests for HGH were introduced.

The NFL's collective bargaining agreement with the players' union also means the league is not allowed to declare which substance a banned player has taken. That leads to a knock-on effect, with players increasingly blaming a positive test on Adderall – a minor but banned stimulant used to treat ADHD – even though there is no way of knowing whether they are telling the truth.

"There's a lack of transparency in the process and that is part of what we are trying to persuade them to alter," said Howman. "But this is what comes about through collective bargaining because you get people holding out for something that may not be to the benefit of the greater good. It's a weakness of the process."

Aldopho Birch, the NFL's senior vice-president of law and labour policy, said he hoped the league's policy would be more open in the future. "We have been proposing the ability to disclose the substance and nature of drugs violations," he said. "Not just to inform the public but as an educational deterrent too."

The players' union, however, believes that player welfare must be the priority. George Atallah, assistant executive director of external affairs at the NFLPA, insists the current protocols catch cheats while also supporting its players. "Our role as a players' union is not just to catch athletes that violate our policy but to protect their rights and confidentiality, and to provide them with the best possible treatment."

Sunday's encounter between the Pittsburgh Steelers and Minnesota Vikings is the first of two NFL matches at Wembley this season. The game, which features last season's most valuable player, Minnesota's Adrian Peterson, is an 80,000 sellout and there is growing talk about a London franchise within the next decade.

But there could be implications for the drug-testing of NFL players in Britain. Wada has no jurisdiction over the NFL's drug policies, and, unless the rules changed, the NFL, rather than the UK anti‑doping agency, would be responsible for testing players from a London franchise.

"We haven't looked at the issue yet but I assume it would be the case," Birch said. "We would need to have consistency in the application of our laws. You can't have one team subject to different laws than everyone else."

However, the NFL insists the lack of repeat offenders shows that their policy is working. "It's somewhat of a misnomer that a four-game suspension is a light penalty," said Birch. "It is a quarter of the season. We also have a very small number of repeat offenders, which suggests to us that missing four games is a high deterrent. But I do agree with Dr Howman when it comes to repeat offenders. Then inadvertence goes out of the window. At that point we need to be very tough about getting them out of our game."

Howman also pinned the lack of a test for human growth hormone in the NFL firmly on the Players Association, claiming: "When drug hormone testing was initially agreed in 2011, we thought that was the best thing the NFL players could do to show the public they were clean. But the Players Association have used every possible way of avoiding testing. That to me is: these protesters have something to hide. Why would you do that if you thought your players were all good guys and all clean and not taking PEDs?"

Howman said a particular stumbling block had been the NFLPA's request for a research project to see if their human growth hormone test was accurate enough on black players. "It's a bit far-fetched so the scientists and the statisticians say but that's what they are hanging out for," he added. "But all the information we've got, and all the studies we've done, tells us it really doesn't warrant that approach."

Birch, meanwhile, insisted that they had made "numerous concessions to the NFLPA" in an effort to obtain agreement on a programme of HGH testing, "but the union won't take yes for an answer".

The union, however, stands by its concerns over the methodology used by Wada in its tests as the reason for the delay in implementation. Atallah said: "We believe the scientific baseline for their HGH test is not accurate and, as in the case of Andrus Veerpalu at the court of arbitration for sport earlier this year, procedural flaws could lead to false positives. Which is why we want a population study. It would be the most scientifically valid baseline in all sports."

Howman fears that significant beefing up of the NFL's anti-doping programme is still some way off. "We are trying to support a programme that is closer to Wada's, but we keep getting told by the players' association to stay away," he said. "It's very difficult for us to take it further as we have no mandate at all."